Let $ G $ be a connected semisimple real algebraic group and $\Gamma <G$ be a Zariski dense discrete subgroup. Let N denote a maximal horospherical subgroup of G, and $P=MAN$ the minimal parabolic subgroup which is the normalizer of N. Let $\mathcal E$ denote the unique P-minimal subset of $\Gamma \backslash G$ and let $\mathcal E_0$ be a $P^\circ $ -minimal subset. We consider a notion of a horospherical limit point in the Furstenberg boundary $ G/P $ and show that the following are equivalent for any $[g]\in \mathcal E_0$ : (1) $gP\in G/P$ is a horospherical limit point; (2) $[g]NM$ is dense in $\mathcal E$ ; (3) $[g]N$ is dense in $\mathcal E_0$ . The equivalence of items (1) and (2) is due to Dal’bo in the rank one case. We also show that unlike convex cocompact groups of rank one Lie groups, the $NM$ -minimality of $\mathcal E$ does not hold in a general Anosov homogeneous space.

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关于高阶齐质空间中星球层的稠密

让 $G$ 是一个连通的半单实代数群并且 $\伽玛 <G$ 是 Zariski 稠密离散子群。让氮表示最大星球面子群G， 和 $P=人$ 最小抛物线子群，它是归一化器氮。让 $\数学E$ 表示唯一的磷- 的最小子集 $\伽玛\反斜杠G$ 然后让 $\数学E_0$ 成为一个 $P^\circ $ -最小子集。我们考虑弗斯滕伯格边界中的星球极限点的概念 $ 毛利率 $ 并证明以下对于任何 $[g]\in \mathcal E_0$ : (1) $gP\in G/P$ 是球面极限点； (2) $[克]NM$ 密集于 $\数学E$ ; (3) $[g]N$ 密集于 $\数学E_0$ 。 项目（1）和（2）的等价性归因于第一级案例中的 Dal'bo。我们还表明，与一级李群的凸余紧群不同， $NM$ - 极小值 $\数学E$ 在一般的阿诺索夫齐次空间中不成立。